Project 03 / 10Propulsion · Design, FEA and testing

Rocket Nozzle

BURPG · Boston University · Fall 2024

A 3D-printed rocket nozzle sized with isentropic flow equations, checked in FEA to a minimum factor of safety of 2.1, and hot-fired on a test stand.

Completed
Mechanical
Simulation

The 3D-printed translucent resin nozzle standing on a table after its hot-fire test, with a scorched, discolored bore and a chipped exit rim — Fig. 01The 3D-printed nozzle after its hot-fire test.

Key result

2.118

Minimum factor of safety

Simulated

From SolidWorks FEA at an 80 psi chamber pressure, against a target of 2. It is a simulation: the printed nozzle was then hot-fired and stayed intact, with a chipped exit rim and a scorched bore.

Technical highlights

Sized from isentropic-flow equations: a 7.2 mm throat, 18.4 mm exit, area ratio of 6.52 and 16.8 mm length.
FEA gave a maximum von Mises stress of 11.9 MPa against a 25.2 MPa yield strength, with a minimum factor of safety of 2.118.
Hot-fired on an aluminum-extrusion test stand with a load cell. The 3D-printed nozzle stayed intact, with heat damage at the exit rim and bore.

My contribution: Team member in a team of 5: design, CAD, FEA, 3D printing and testing
Part drawings and the assembly with the adapter and 1 inch NPT chamber nipple
Tools: SolidWorksSolidWorks FEA3D printing (ABS-like resin)Arduino Uno

Overview

A team project with Boston University Rocket Propulsion Group (BURPG) to design and 3D print a rocket nozzle, plus the electronics to hot-fire it. Flow calculations sized the nozzle, SolidWorks FEA showed a minimum factor of safety of 2.1 at an 80 psi chamber pressure, and the printed nozzle was then hot-fired on a test stand.

The hot-fire test, filmed in the fume hood.

Engineering challenge

The brief was to build a rocket nozzle from a set of initial constraints, along with the electronics needed to hot-fire it and record thrust. The test was a static firing, so mass wasn't a design driver.

Design process

We built a spreadsheet from the textbook equations to size the nozzle from chamber pressure, assuming isentropic flow. It gave a specific impulse of 274.6 s, an exit velocity of 2,691 m/s, a critical pressure ratio of 0.578 (about 46 psi at the throat with an 80 psi chamber), an area ratio of 6.52, a 7.2 mm throat diameter, an 18.4 mm exit diameter and a 16.8 mm length (an 80% length nozzle).

In SolidWorks the nozzle mates to an adapter on a 1 inch NPT chamber nipple through six 1/4-20 bolts and nuts. The calculated dimensions drive the geometry, and the part weighs 0.04 kg.

For the FEA we built a custom material from the resin's data sheet, taking yield strength as 70% of tensile strength (25.2 MPa). We applied 80 psi chamber pressure and about 46 psi throat pressure, with the six bolt-hole faces fixed.

The test electronics use an Arduino Uno with a load cell and HX711 amplifier to record thrust, an SD card board to log the data, and a push button that starts the sequence. Relays switch the 12 V solenoid and the e-match, with a diode across the solenoid to block back-current.

Fabrication & assembly

We compared machining the part on a lathe, which is good experience but slow and impractical for several groups, with 3D printing, which only needs the CAD model but raised a concern about melting during the firing. We chose 3D printing in ABS-like resin. Heat transfer wasn't simulated, so we thickened the throat as a precaution and set the wall thickness at 0.1 in.

For the firing, the chamber and nozzle were mounted on an aluminum-extrusion test stand inside a fume hood, with the load cell in line to measure thrust.

Testing & results

What the analysis said, and what the test showed

Simulated or calculated

Predicted

Thrust at optimal expansion: 35.0 N (calculated)
Thrust at sea level: 11.8 N (calculated)
Peak stress: 11.9 MPa vs 25.2 MPa yield (simulated)
Minimum factor of safety: 2.118 (simulated, target 2)

Observed in the test

Observed

Structure: Printed part stayed intact
Exit rim: Chipped
Bore: Scorched
Test setup: Nozzle on a test stand in a fume hood, with a load cell in line

The stress analysis checks the structure at pressure only, because heat transfer wasn't simulated. The damage seen after the firing is a thermal effect, which is what the simulation did not cover.

After the hot fire

What the fired hardware looks like. Heat transfer wasn't simulated, so heat damage was a risk we had flagged when we chose to 3D print the nozzle, and we thickened the throat as a precaution.

Chipped exit rim
Afterward the exit rim was chipped. This is the kind of heat damage we had flagged as a risk of printing the part.
Scorched bore
The bore is scorched and discolored where the hot gas passed through.
Flange intact
The flange with its bolt holes stayed intact, and the printed part held together through the firing.

Calculated performance: 35.0 N of thrust at the optimal expansion and 11.8 N at sea level. The FEA gave a maximum von Mises stress of 11.9 MPa against the 25.2 MPa yield strength, and a minimum factor of safety of 2.118, above our target of 2, with most of the part above 3.

We hot-fired the nozzle on the test stand (video above). The printed part stayed intact: afterward its exit rim was chipped and its bore was scorched, which is the kind of heat damage we had flagged as a risk of printing it.

Gallery

A hand holding the fired nozzle up to the camera, showing the flange with its six bolt holes, the scorched bore and the chipped exit rim — Fig. 03The nozzle after the test: the exit rim is chipped and the bore is scorched, but the part stayed intact.

The test stand inside a fume hood before the firing: an aluminum-extrusion frame holding the chamber and nozzle, a load cell, brass valve fittings and wiring — Fig. 04The test stand before the firing, inside a fume hood: the chamber and nozzle on an aluminum-extrusion frame, with a load cell, valve fittings and wiring.

Five team members posing in front of the Boston University Rocket Propulsion Group door, one holding up the nozzle — Fig. 05The BURPG team outside the lab, with the nozzle.

CAD render of the nozzle assembly, labeled: the nozzle (geometry hidden), the adapter, the 1 inch NPT chamber nipple, and the 1/4-20 nuts and bolts — Fig. 06The assembly in CAD: the nozzle bolts to an adapter on a 1 inch NPT chamber nipple.

Exploded CAD view of the nozzle and adapter with six bolts and nuts — Fig. 07Exploded view: the nozzle and adapter are joined with six 1/4-20 bolts and nuts.

Engineering drawing of the nozzle with a section view, detail views and critical dimensions — Fig. 08Part drawing, dimensioned from the calculated throat, exit and length values.

Engineering drawing of the nozzle and adapter assembly with a section view, a detail of the sealing region, an isometric view and an exploded view — Fig. 09Nozzle and adapter drawing: section view, sealing detail and exploded view.

Section view of the nozzle showing pressure loads as red arrows and fixed bolt-hole faces in green — Fig. 10FEA setup: 80 psi chamber pressure, about 46 psi at the throat, and the bolt-hole faces fixed.

SolidWorks von Mises stress plot of the nozzle, with the highest stresses around the bolt holes — Fig. 11Von Mises stress: 11.9 MPa maximum against a 25.2 MPa yield strength.

SolidWorks factor of safety plot of the nozzle with a minimum of 2.118 near a bolt hole and most of the part above 3 — Fig. 12Factor of safety: 2.118 at the minimum, with most of the part above 3.

Circuit schematic of the hot-fire electronics: Arduino Uno, load cell amplifier, SD card board, relays, solenoid and e-match — Fig. 13Hot-fire electronics: Arduino, load cell, SD card logging, and relays for the solenoid and e-match.